Abstract
For an archetypal two-degree-of-freedom forced oscillator, relevant to a large class of mechanical problems, we examine the patterns of bifurcation that govem the internal 1:2 resonance of the system. A knowledge of these bifurcations allows the counter-intuitive suppression and control of escape by internal modal interactions. The bifurcations examined include symmetry-breaking pitchforks, Neimark bifurcations (secondary Hopf bifurcations) to a toroidal attractor, and chaotic crises which trigger dangerous large-amplitude excursions. We particularly focus on the effect that a symmetry-breaking imperfection has on the suppression of escape.
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van der Heijden, G., Thompson, J. (2005). Patterns of Bifurcation Suppressing Escape at Internal Resonance. In: Rega, G., Vestroni, F. (eds) IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics. Solid Mechanics and its Applications, vol 122. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3268-4_7
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DOI: https://doi.org/10.1007/1-4020-3268-4_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3267-7
Online ISBN: 978-1-4020-3268-4
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